Fast noniterative orbital localization for large molecules

Aquilante, Francesco; Pedersen, Thomas Bondo; Merás, Alfredo Sánchez de; Koch, Henrik

doi:10.1063/1.2360264

Cited by 163 publications

(197 citation statements)

References 42 publications

(64 reference statements)

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“…67,68 To expedite the evaluation of the exchange Fock matrix, we employ the local-K ͑LK͒ screening 69 with localized Cholesky molecular orbitals. 70 …”

Section: Resultsmentioning

confidence: 99%

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Aquilante

Gagliardi

Pedersen

et al. 2009

The Journal of Chemical Physics

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221

274

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Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation ͓F. Aquilante et al., J. Chem. Phys. 127, 114107 ͑2007͔͒. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

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“…67,68 To expedite the evaluation of the exchange Fock matrix, we employ the local-K ͑LK͒ screening 69 with localized Cholesky molecular orbitals. 70 …”

Section: Resultsmentioning

confidence: 99%

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Aquilante

Gagliardi

Pedersen

et al. 2009

The Journal of Chemical Physics

Self Cite

221

274

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“…Aquilante et al 28 exploited the locality of the density matrix to generate local orbitals by Cholesky decomposing the density. Cholesky orbitals are computed in a non-iterative manner, but it relies on the ordering of the AOs.…”

Section: Localization Function Optimizationmentioning

confidence: 99%

Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals

2016

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The scope of this review article is to discuss the locality of occupied and virtual orthogonal Hartree-Fock orbitals generated by localization function optimization. Locality is discussed from the stand that an orbital is local if it is confined to a small region in space. Focusing on locality measures that reflects the spatial extent of the bulk of an orbital and the thickness of orbital tails, we discuss, with numerical illustrations, how the locality may be reported for individual orbitals as well as for sets of orbitals. Traditional and more recent orbital localization functions are reviewed, and the locality measures are used to compare the locality of the orbitals generated by the different localization functions, both for occupied and virtual orbitals. Numerical illustrations are given also for large molecular systems and for cases where diffuse functions are included in the atomic orbital basis. In addition, we have included a discussion on the physical and mathematical limitations on orbital locality.

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“…The quartic scaling is due to the evaluation of the exchange terms which require also a MO half-transformation of the vectors, L J → L k J . By using the recently developed "local exchange" ͑LK͒ screening 16 in conjunction with localized Cholesky MOs, 53 the actual scaling of this step is reduced to quadratic even in compact molecules. 16 The construction of the Q matrix is done without explicit construction of the MO-transformed ERIs.…”

Section: ͑11͒mentioning

confidence: 99%

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Aquilante

Pedersen

Lindh

et al. 2008

The Journal of Chemical Physics

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207

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Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field ͑CASSCF͒ method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra--acetato-dicopper͑II͒, and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.

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Fast noniterative orbital localization for large molecules

Cited by 163 publications

References 42 publications

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

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